diff --git a/src/backend/commands/tablecmds.c b/src/backend/commands/tablecmds.c
index a3c7e26190b..015e11af67b 100644
--- a/src/backend/commands/tablecmds.c
+++ b/src/backend/commands/tablecmds.c
@@ -12966,6 +12966,14 @@ ATPostAlterTypeCleanup(List **wqueue, AlteredTableInfo *tab, LOCKMODE lockmode)
 		Oid			relid;
 
 		relid = IndexGetRelation(oldId, false);
+
+		/*
+		 * As above, make sure we have lock on the index's table if it's not
+		 * the same table.
+		 */
+		if (relid != tab->relid)
+			LockRelationOid(relid, AccessExclusiveLock);
+
 		ATPostAlterTypeParse(oldId, relid, InvalidOid,
 							 (char *) lfirst(def_item),
 							 wqueue, lockmode, tab->rewrite);
@@ -12982,6 +12990,20 @@ ATPostAlterTypeCleanup(List **wqueue, AlteredTableInfo *tab, LOCKMODE lockmode)
 		Oid			relid;
 
 		relid = StatisticsGetRelation(oldId, false);
+
+		/*
+		 * As above, make sure we have lock on the statistics object's table
+		 * if it's not the same table.  However, we take
+		 * ShareUpdateExclusiveLock here, aligning with the lock level used in
+		 * CreateStatistics and RemoveStatisticsById.
+		 *
+		 * CAUTION: this should be done after all cases that grab
+		 * AccessExclusiveLock, else we risk causing deadlock due to needing
+		 * to promote our table lock.
+		 */
+		if (relid != tab->relid)
+			LockRelationOid(relid, ShareUpdateExclusiveLock);
+
 		ATPostAlterTypeParse(oldId, relid, InvalidOid,
 							 (char *) lfirst(def_item),
 							 wqueue, lockmode, tab->rewrite);
diff --git a/src/test/regress/expected/alter_table.out b/src/test/regress/expected/alter_table.out
index 20b7b3c651e..3305c6ed24a 100644
--- a/src/test/regress/expected/alter_table.out
+++ b/src/test/regress/expected/alter_table.out
@@ -4587,6 +4587,14 @@ create table attbl(a int);
 create table atref(b attbl check ((b).a is not null));
 alter table attbl alter column a type numeric;  -- someday this should work
 ERROR:  cannot alter table "attbl" because column "atref.b" uses its row type
+alter table atref drop constraint atref_b_check;
+create statistics atref_stat on ((b).a is not null) from atref;
+alter table attbl alter column a type numeric;  -- someday this should work
+ERROR:  cannot alter table "attbl" because column "atref.b" uses its row type
+drop statistics atref_stat;
+create index atref_idx on atref (((b).a));
+alter table attbl alter column a type numeric;  -- someday this should work
+ERROR:  cannot alter table "attbl" because column "atref.b" uses its row type
 drop table attbl, atref;
 /* End test case for bug #18970 */
 -- Test that ALTER TABLE rewrite preserves a clustered index
diff --git a/src/test/regress/sql/alter_table.sql b/src/test/regress/sql/alter_table.sql
index fc9396472d1..b7aa3ee179f 100644
--- a/src/test/regress/sql/alter_table.sql
+++ b/src/test/regress/sql/alter_table.sql
@@ -3027,6 +3027,14 @@ drop table attbl, atref;
 create table attbl(a int);
 create table atref(b attbl check ((b).a is not null));
 alter table attbl alter column a type numeric;  -- someday this should work
+alter table atref drop constraint atref_b_check;
+
+create statistics atref_stat on ((b).a is not null) from atref;
+alter table attbl alter column a type numeric;  -- someday this should work
+drop statistics atref_stat;
+
+create index atref_idx on atref (((b).a));
+alter table attbl alter column a type numeric;  -- someday this should work
 drop table attbl, atref;
 
 /* End test case for bug #18970 */